
Mathematics 2008
An equivariant index formula for almostCR manifoldsDOI: 10.1093/imrn/rnp057 Abstract: We consider a consider the case of a compact manifold M, together with the following data: the action of a compact Lie group H and a smooth Hinvariant distribution E, such that the Horbits are transverse to E. These data determine a natural equivariant differential form with generalized coefficients J(E,X) whose properties we describe. When E is equipped with a complex structure, we define a class of symbol mappings in terms of the resulting almostCR structure that are Htransversally elliptic whenever the action of H is transverse to E. We determine a formula for the Hequivariant index of such symbols that involves only J(E,X) and standard equivariant characteristic classes. This formula generalizes the formula given in arXiv:0712.2431 for the case of a contact manifold.
